Trajectory Optimization Under Stochastic Dynamics Leveraging Maximum Mean Discrepancy

This paper addresses sampling-based trajectory optimization for risk-aware navigation under stochastic dynamics. Typically such approaches operate by computing perturbed rollouts around the nominal dynamics to estimate the collision risk associated with a sequence of control commands. We consider a setting where it is expensive to estimate risk using perturbed rollouts, for example, due to expensive collision-checks. We put forward two key contributions. First, we develop an algorithm that distills the statistical information from a larger set of rollouts to a reduced-set with sample size . Consequently, we estimate collision risk using just rollouts instead of . Second, we formulate a novel surrogate for the collision risk that can leverage the distilled statistical information contained in the reduced-set. We formalize both algorithmic contributions using distribution embedding in Reproducing Kernel Hilbert Space (RKHS) and Maximum Mean Discrepancy (MMD). We perform extensive benchmarking to demonstrate that our MMD-based approach leads to safer trajectories at low sample regime than existing baselines using Conditional Value-at Risk (CVaR) based collision risk estimate.
View on arXiv@article{sharma2025_2501.19045, title={ Trajectory Optimization Under Stochastic Dynamics Leveraging Maximum Mean Discrepancy }, author={ Basant Sharma and Arun Kumar Singh }, journal={arXiv preprint arXiv:2501.19045}, year={ 2025 } }